非线性时延网络控制系统的模糊建模与控制

针对时变网络诱导时延小于一个采样周期的非线性时延网络控制系统,讨论系统的稳定性及控制器的设计方法.利用基于“IF-THEN”规则的模糊模型近似系统中的非线性,将时延的不确定性转化为系统参数的不确定性,从而将此类非线性网络控制系统建模为一类具有参数不确定性的离散Takagi-Sugeno（T-S）模糊模型.基于建立的模型,利用Lyapunov方法和线性矩阵不等式方法,分析了系统的稳定性及模糊状态反馈控制器的设计方法,最后通过仿真实例验证了所提出方法的有效性.     

室内热舒适环境的模糊关系矩阵模型控制系统

针对复杂非线性系统中多个输出不能解耦的控制问题,基于实际系统的采样数据,利用矩阵半张量积运算建立模糊关系矩阵模型,得出一种新型模糊控制器设计方法.将传统模糊控制中的推理过程和模糊规则的建立转化成矩阵运算,有效避免了建模和控制的复杂性.将其应用于室内热环境舒适度控制系统中,基于室内外的温度、湿度等多个变量的采样数据对,给出具体的模糊关系矩阵的建立过程,设计得出新型模糊控制器.仿真和实验结果表明,该方法能够实现室内热环境的舒适度控制,并且不需要进行多变量之间的解耦.     

基于T–S模糊模型的非线性系统鲁棒采样控制

使用模糊采样控制方法研究一类T–S(Takagi-Sugeno)模糊模型描述的非线性系统鲁棒镇定问题. 首先, 充分 利用整个采样区间[tk; tk+1) 的特征信息, 构造出一个改进的双边时间相关Lyapunov 泛函. 然后, 结合提出的 Lyapunov泛函和自由矩阵不等式, 导出了确保非线性系统渐近稳定的鲁棒镇定条件, 并给出模糊采样控制器设计方 法. 最后, 通过4个例子仿真验证了提出方法的有效性和优越性.     

不确定非线性网络化系统的鲁棒H_∞控制

用T-S(Takagi-Sugeno)模糊方法研究了带有参数不确定的非线性网络化系统的鲁棒控制.首先,考虑到诱导时延和数据丢包等网络因素的影响,基于事件驱动的保持器的更新序列建立闭环反馈系统的采样模型,并将其转化为状态中附加两个时滞变量的连续T-S模糊系统.然后,利用时滞系统方法,分析不确定闭环模糊系统的鲁棒H∞性能,并设计相应的鲁棒H∞模糊控制器.最后,仿真例子表明了方法的有效性.     

变采样周期网络控制系统的H∞控制

时延以及数据包丢失是导致网络控制系统性能降低的重要原因.利用既是时钟驱动又是事件驱动的传感器,可以使时延与采样周期具有相同的长度,这样降低了建模随机时延的保守性.通过把具有时变采样周期的网络控制系统建模为切换系统,并利用线性矩阵不等式,本文给出了保证系统渐进稳定的充分条件,同时设计了系统的H∞控制器,仿真结果表明了本文所提出的变采样周期方法的有效性.     

非线性系统的鲁棒采样控制

研究在汽车转向控制中遇到的、具有输出约束的一类非线性不确定系统的鲁棒采样 控制和鲁棒采样最优控制问题,结果表示为一些矩阵不等式.最后基于线性矩阵不等式,给出 了一个迭代算法和算例.数值计算实例证明了该算法的有效性.     

带有随机时延的非线性网络控制系统的输出反馈镇定

考虑了一类非线性网络控制系统的输出反馈镇定问题.通过齐次马尔可夫链来描述采样器-控制器和控制器.执行器的时延,将网络控制系统建模为带跳非线性系统.利用Lyapunov方法和线性矩阵小等式技巧,得到了闭环系统随机稳定的充分条件,并给出了镇定控制器的设计方法.     

网络控制系统的时延仿真研究与控制器设计

针对网络控制系统(NCS)中的随机时延问题,根据实际网络时延的分布情况,提出了一种新的具有随机时延的网络控制系统的建模方法-离散T-S模型,并用并行分布补偿原理(PDC)设计模糊控制器.同时提出一种新的模糊控制系统隶属函数的确定方法,利用Lyapunov定理和线性矩阵不等式(LMI)研究了系统的稳定性问题,给出基于LMI的模糊控制器的设计方法.最后通过仿真实例证明控制方法能够使具有时延的网络控制系统稳定.     

基于θ-D方法的欠驱动TORA系统非线性最优控制

针对TORA (Translational oscillator with rotating actuator)系统的镇定控制问题, 提出一种基于$\theta $-D方法的非线性最优控制方案.应用拉格朗日方程建立TORA系统的数学模型, 为保证状态空间形式的TORA系统数学模型中状态向量系数矩阵$A(\pmb{x})$能够分离出常值矩阵, 且其能与控制位置矩阵构成可控对, 采用不同于传统形式的解耦坐标变换对TORA系统进行了处理, 以此为基础为TORA系统设计基于$\theta $-D方法的非线性最优控制器, 该控制方案可离线得到控制输入的显示表达式.通过数值仿真以及与基于局部线性化的线性最优控制方案进行比较, 验证了所提非线性最优控制方案所具有的良好瞬态性能.     

使用鲁棒控制器稳定模糊系统模型

将非线性系统用T-S模糊动态模型描述,并将全局模糊系统模型表示成不确定系统形式采用新的鲁棒控制器设计方法,设计出使全局模糊系统模型渐近稳定的线性控制器避免了并行分配补偿法中求解公共矩阵P的困难.一级倒立摆的模糊控制器设计实例,证明了方案的简洁有效.     

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz–Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.     

Exponential sampled-data control for T–S fuzzy systems: application to Chua's circuit

ABSTRACT

This study deals with the chaotic phenomenon of nonlinear Chua's circuit for power generator systems. Takagi–Sugeno (T–S) fuzzy model of a nonlinear system is established. By constructing a suitable Lyapunov functional, exponential stability conditions are obtained for fuzzy systems. Based on the sampled-data control theory, extreme sensitivity is visualised in the state trajectory depending on the initial conditions and sampled-data fuzzy controllers are designed in the form of linear matrix inequality (LMI). Finally, some numerical simulation results are shown that the sampled-data fuzzy control system adopts a well-designed methodology.     

Sampled-Data Asynchronous Fuzzy Output Feedback Control for Active Suspension Systems in Restricted Frequency Domain

This paper proposes a novel sampled-data asynchronous fuzzy output feedback control approach for active suspension systems in restricted frequency domain.In order to better investigate uncertain suspension dynamics,the sampleddata Takagi-Sugeno(T-S)fuzzy half-car active suspension(HCAS)system is considered,which is further modelled as a continuous system with an input delay.Firstly,considering that the fuzzy system and the fuzzy controller cannot share the identical premises due to the existence of input delay,a reconstructed method is employed to synchronize the time scales of membership functions between the fuzzy controller and the fuzzy system.Secondly,since external disturbances often belong to a restricted frequency range,a finite frequency control criterion is presented for control synthesis to reduce conservatism.Thirdly,given a full information of state variables is hardly available in practical suspension systems,a two-stage method is proposed to calculate the static output feedback control gains.Moreover,an iterative algorithm is proposed to compute the optimum solution.Finally,numerical simulations verify the effectiveness of the proposed controllers.     

Stabilization of Nonlinear Systems Under Variable Sampling: A Fuzzy Control Approach

This paper investigates the problem of stabilization for a Takagi-Sugeno (T-S) fuzzy system with nonuniform uncertain sampling. The sampling is not required to be periodic, and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound. By using the input delay approach, the T-S fuzzy system with variable uncertain sampling is transformed into a continuous-time T-S fuzzy system with a delay in the state. Though the resulting closed-loop state-delayed T-S fuzzy system takes a standard form, the existing results on delay T-S fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay. A new condition guaranteeing asymptotic stability of the closed-loop sampled-data system is derived by a Lyapunov approach plus the free weighting matrix technique. Based on this stability condition, two procedures for designing state-feedback control laws are given: one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints, which can be readily solved using standard numerical software. An illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology.     

Takagi-Sugeno模糊连续系统的模糊采样控制

研究了T-S模糊连续系统的模糊采样控制问题．利用广义系统的描述方法、Lyapunov-Krasovikii泛函以及线性矩阵不等式(LMI)方法,建立了LMIs形式的依赖于采样时间间隔的模糊采样镇定条件,同时给出了模糊采样控制律的设计方法．所设计的模糊采样控制律可以镇定T-S模糊系统．而且,当连续时间模糊控制律可以镇定T-S模糊系统时,对于足够小的采样时间间隔,带有同样增益矩阵的模糊采样控制律也可以镇定T-S模糊系统．最后,通过两个仿真实例说明了所给方法的有效性．     

基于双边闭环函数的网络化采样控制系统稳定性分析EI北大核心CSCD

考虑数据通信时延不确定环境下网络化采样控制系统的稳定性问题.首先基于输入时滞方法,建立包含采样周期信息的网络化采样控制系统的数学模型,在此基础上,采用双边闭环函数方法和自由矩阵积分不等式技术,得到网络传输时滞变化区间依赖稳定性新准则,并进一步讨论了网络化采样控制系统中网络时延与采样周期之间的关系.仿真结果表明减小采周期可以增强网络控制系统对网络通信时延的鲁棒性.     

Intelligent digital redesign for nonlinear systems using a guaranteed cost control method

In this paper, a novel intelligent digital redesign (IDR) technique using the guaranteed cost control method is proposed for nonlinear systems which can be represented by a Takagi-Sugeno (T-S) fuzzy model. The IDR technique, which is one of the sampled-data fuzzy controller design methods, guarantees not only the stability condition of the sampled-data closed-loop system with the sampleddata fuzzy controller and the state-matching error is presented. By using the concept of the guaranteed cost control method, sufficient conditions are obtained for both minimization of the state-matching error and stabilization of the sampled-data closed-loop system and derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to verify the effectiveness of the proposed technique.     

Robust sampled-data control with random missing data scenario

The problem of robust sampled-data control for uncertain dynamic systems in the presence of missing data has been investigated. By using stochastic variables with a Bernoulli distributed white sequence to model missing data, along with time-varying norm-bounded uncertainties, and the input delay approach for sampled-data systems, two models for the considered sampled-data control system are proposed as the consecutive missing data scenario. Moreover, when data are missing, the control signals are held as the last received data. Sufficient conditions for the existence of desired robust sampled-data controllers are presented in the form of a linear matrix inequality. A numerical example is given to illustrate the validity of the proposed methods and to compare the results between the two proposed models of the sampled-data control system.